Question

Given H(6, 7) and I(-7,-6), if point G lies 1/2 of the way along Hl. John says that point G is located at the origin. Is John correct? Justify your answer.

Answer 1

Given:

Two points are (6, 7) and I(-7,-6).

Point G lies $\dfrac{1}{2}$ of the way along Hl.

John says that point G is located at the origin.

To find:

Whether John is correct or not.

Solution:

Point G lies $\dfrac{1}{2}$ of the way along Hl. I means point G is the midpoint of HI.

$Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

$G=\left(\dfrac{6-7}{2},\dfrac{7-6}{2}\right)$

$G=\left(\dfrac{-1}{2},\dfrac{1}{2}\right)$

The location of point G is at $\left(\dfrac{-1}{2},\dfrac{1}{2}\right)$, which is not equal to origin, i.e., (0,0).

Therefore, John is incorrect.